Compound Interest Guide
The Compound Interest Formula
A = P (1 + r/n)nt
+ M × [((1 + r/n)nt − 1) ÷ (r/n)] (with monthly contributions)
A = Final amount
P = Principal (starting $)
r = Annual interest rate
n = Compounding periods/yr
t = Time in years
M = Monthly contribution
Try a scenario:
Final Balance
—
Your Money In
—
Interest Earned
—
Your contributions — Free money (interest) —
—
Adjust Variables
Principal (P)
$
Annual Rate (r)
%
Reality check: savings ≈ 1–4% · S&P 500 avg ≈ 10% · inflation ≈ 3%
Years (t)
yrs
Compounding (n)
Monthly Contribution (M) $100
$
Growth Multiplier
—
times what you put in
Balance Over Time
Total Balance Money You Put In Principal Only
The Cost of Waiting
Time is the most powerful variable in the formula — here's the proof.
Same rate, same monthly deposit. The only difference is when you start.
Start Today
—
invest for the full time
Start in 10 yrs
—
fewer years to grow
What Waiting Costs
—
left on the table
—
Rule of 72
A mental math shortcut for doubling time
Years to double ≈ 72 ÷ annual interest rate
Interest Rate 7.0%
Synced with annual rate above ↑
The Rule of 72 is a quick estimate — not exact, but remarkably close for rates between 6–10%. It works because of the natural logarithm hidden inside compound growth.
Exact formula: t = ln(2) ÷ ln(1 + r)
≈ 0.693 ÷ r ≈ 72 ÷ (100r)
10.3
years to double your money
at 7% annual return
Exact value
10.24 years